Abstract
Let denote the set of symmetric matrices over some semiring . The set, , of elements of that are a finite sum of squares of elements in , is called the positive subsemiring of . A matrix, B, with entries in is primitive if some power of B has all nonzero entries. We characterize those linear operators on the set of symmetric matrices over that map the set of primitive matrices to itself and the set of nonprimitive matrices to itself. We also characterize those linear operators on the set of symmetric matrices over that map the set of primitive matrices whose square has all nonzero entries to itself and the complement of that set to itself. The characterization of linear preservers of real symmetric primitive matrices follows as a special case.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
